laplace                 package:VGAM                 R Documentation

_L_a_p_l_a_c_e _D_i_s_t_r_i_b_u_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Maximum likelihood estimation of the 2-parameter Laplace
     distribution.

_U_s_a_g_e:

     laplace(llocation="identity", lscale="loge",
             elocation=list(), escale=list(),
             ilocation=NULL, iscale=NULL,
             method.init=1, zero=NULL)

_A_r_g_u_m_e_n_t_s:

llocation, lscale: Character. Parameter link functions for location
          parameter a and scale parameter b. See 'Links' for more
          choices.

elocation, escale: List. Extra argument for each of the links. See
          'earg' in 'Links' for general information.

ilocation, iscale: Optional initial values. If given, it must be
          numeric and values are recycled to the appropriate length.
          The default is to choose the value internally. 

method.init: Initialization method. Either the value 1 or 2.

    zero: An integer-valued vector specifying which linear/additive
          predictors are modelled as intercepts only. The value
          (possibly values) must be from the  set {1,2} corresponding
          respectively to a and b. By default all linear/additive
          predictors are modelled as a linear combination of the
          explanatory variables.

_D_e_t_a_i_l_s:

     The Laplace distribution is often known as the
     _double-exponential_ distribution and, for modelling, has heavier
     tail than the normal distribution. The Laplace density function is

                   f(y) =  (1/(2b)) exp( -|y-a|/b )

     where -Inf<y<Inf, -Inf<a<Inf and b>0. Its mean is a and its
     variance is 2b^2.

     For 'y ~ 1' (where 'y' is the response) the maximum likelihood
     estimate (MLE) for the location parameter is the sample median,
     and the MLE for b is 'mean(abs(y-location))' (replace location by
     its MLE if unknown).

_V_a_l_u_e:

     An object of class '"vglmff"' (see 'vglmff-class'). The object is
     used by modelling functions such as 'vglm' and 'vgam'.

_W_a_r_n_i_n_g:

     This family function has not been fully tested. The MLE regularity
     conditions do not hold for this distribution, therefore misleading
     inferences may result, e.g., in the 'summary' and 'vcov' of the
     object.

_N_o_t_e:

     This family function uses Fisher scoring. Convergence may be slow
     for non-intercept-only models; half-stepping is frequently
     required.

_A_u_t_h_o_r(_s):

     T. W. Yee

_R_e_f_e_r_e_n_c_e_s:

     Kotz, S., Kozubowski, T. J. and Podgorski, K. (2001) _The Laplace
     distribution and generalizations: a revisit with applications to
     communications, economics, engineering, and finance_, Boston:
     Birkhauser.

_S_e_e _A_l_s_o:

     'rlaplace'.

_E_x_a_m_p_l_e_s:

     y = rlaplace(n <- 100, loc=2, scale=exp(1))
     fit = vglm(y  ~ 1, laplace, trace=TRUE, crit="l")
     coef(fit, matrix=TRUE)
     Coef(fit)
     median(y)

     x = runif(n <- 1001)
     y = rlaplace(n, loc=2, scale=exp(-1+1*x))
     fit = vglm(y  ~ x, laplace(iloc=0.2, meth=2, zero=1), trace=TRUE)
     coef(fit, matrix=TRUE)

